A short proof of Dvoretzky's theorem on almost spherical sections of convex bodies
T. Figiel (1976)
Compositio Mathematica
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T. Figiel (1976)
Compositio Mathematica
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S. J. Szarek (1979-1980)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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J. Lindenstrauss (1975-1976)
Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")
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A. Pełczyński (1976)
Studia Mathematica
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Stanisłlaw Szarek, Nicole Tomczak-Jaegermann (1980)
Compositio Mathematica
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Baronti, Marco, Papini, Pier Luigi (1992)
Mathematica Pannonica
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Alexander E. Litvak, Vitali D. Milman, Nicole Tomczak-Jaegermann (2010)
Studia Mathematica
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In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]-dimensional subspace which has further proportional-dimensional Euclidean subspaces of any proportion. We consider a space X₁ = (ℝⁿ,||·||₁) with the property that if a space X₂ = (ℝⁿ,||·||₂) is "not too far" from X₁ then there exists a [λn]-dimensional subspace E⊂ ℝⁿ such that E₁ = (E,||·||₁)...
Dorn, C. (1978)
Portugaliae mathematica
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Victor Klee, Libor Veselý, Clemente Zanco (1996)
Studia Mathematica
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For combining two convex bodies C and D to produce a third body, two of the most important ways are the operation ∓ of forming the closure of the vector sum C+D and the operation γ̅ of forming the closure of the convex hull of C ⋃ D. When the containing normed linear space X is reflexive, it follows from weak compactness that the vector sum and the convex hull are already closed, and from this it follows that the class of all rotund bodies in X is stable with respect to the operation...
D. R. Lewis (1983)
Compositio Mathematica
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